Direct Torque Control of a Doubly Fed Induction Generator of Wind Turbine for Maximum Power Extraction Anass.Bakouri Mohammed V University Agdal Department of Electrical Engineering, Mohammadia School of Engineers Rabat,Morocco
[email protected]
Ahmed. Abbou, Hassan. Mahmoudi Mohammed V University Agdal Department of Electrical Engineering Mohammadia School of Engineers Rabat,Morocco
[email protected],
[email protected],
Abstract—In this paper we present the control system of a wind turbine based doubly fed induction generator (DFIG) by direct torque control (DTC). The wind energy conversion system (WECS) equipped with wind turbine, DFIG, DC bus and the power convector. The converter is controlled to generate the maximum power from wind turbine generator (WTG) by using maximum power point tracking (MPPT) strategy. The pitch control is also proposed to limit the generator power at its rated value. The DTC is developed to regulate the flux and torque. The simulation results of a 1.5MW doubly fed induction generator show the performances of the control strategy proposed. These results are validated by using the MATLAB/Simulink environment
This work is structured as follows. In Section 2 we start by modeling of the wind turbine and DFIG. In Section 3, a tracking technique operating point at maximum power point tracking (MPPT) and the pitch control when the wind speed is higher than the rated wind speed will be presented. In Section 4, the control strategy of DTC. The simulations results in Section 5. Finally a conclusion is presented in section 6.
Transformer
Keywords- Doubly fed induction generator (DFIG); direct torque control (DTC); Maximum power point tracking (MPPT); wind turbine generator (WTG); wind energy conversion system (WECS)
I.
Grid
DFIG
Gear box
INTRODUCTION
Wind energy is one of the most Promising and important sources of renewable energy in the worldwide, mainly because it is a clean energy, cost-effective, renewable, friendly to environment and also its contribution for the reduction of CO2 emissions. Currently, wind power systems that are based on doubly fed induction generators (DFIGs), which are controlled by back-to- back power converters, constitute almost 50% of the installed wind turbines (WTs) [1]. The main advantage of the DFIG is that the power converter transmits only a fraction of the total power (20-30%) [2]. This means that the dimensioning, the losses in the power converters, as well as the cost, are reduced .The stator windings of DFIG are directly connected to the grid, and rotor windings are connected to the grid through a back-to-back converter (Fig.1). This paper proposes The DTC method directly controls the torque and flux of DFIG by selecting voltage vectors from a look-up table according to the logical output of the torque and flux hysteresis controllers for maximum power extract from wind turbine generator (WTG) [3]. It minimizes the use of machine parameters and reduces the complexity of vector control algorithm [4].
Kamal.Elyaalaoui Mohammed V University Agdal Department of Electrical Engineering Mohammadia School of Engineers Rabat,Morocco
[email protected]
DC AC
AC DC
Fig1. Schematic diagram of a DFIG
II.
WIND TURBINE MODELING
The aerodynamic power captured by the aeroturbine rotor is given by the following expression [5]. = 0.5
( , )
(1)
Where is the air density, A is the area of the wind wheel (m2) Vw is the wind speed (m/s), Cp ( ) is the power coefficient of the turbine, is the tip speed ratio and is the pitch angle. The tip speed ratio is given by the following equation: . = (2) Where
is the rotor speed.
IV.
The turbine torque is given by: =
(3)
Where is turbine speed For the used turbine, this coefficient of power is expressed as is given by the following mathematical [6]. C ( ) = 0.5176 0.4 5 + 0.0068
In order to tracking an optimal rotor speed reference, the MPPT algorithm is proposed based in PI controller . The objective of the MPPT operation mode is to maximize power extraction at low to medium wind speeds by following the maximum value of the wind power . To extract the maximum power, we need to fix The tip speed ratio at opt , the maximum power coefficient C p max and should be equal to 0° [9].
(4)
Where
is given by 1 =
1 + 0.08.
0.035 +1
R opt
(5)
0.48
and
opt
m opt
are the tip speed ratio and the rotor
speed optimal respectively. The aerodynamic power optimal must be set to the following expression
pw
0 . 5C p
opt
R
A
max
3 m opt
(15)
opt
Beta=0° 0,4
2
x 10
6
Maximum power point
Beta=5° 0,3
Vw= 12m/s
Beta=10°
1.5
0,2
Beta=20° 0,1
0 0
5
8.1 10 15 Tip speed ratio ,Lumbda
20
The DFIG is described in the Park d–q frame by the following set of equations [7] [8] : = + (6) =
+
1
Vw= 9m/s Vw= 7m/s Vw= 5m/s
III. DFIG MODELLING
+
Vw= 11m/s
0.5
Fig. 2 Wind turbine characteristic curves
=
M e c h a n ic a l p o w e r ( w )
P o w e r c o e ffic ie n t , C p
(14)
m opt
Vw
Where
The variation of the power coefficient versus for a constant value of the pitch angle in the case of a variable speed is illustrated in Fig. 2.The maximum value of Cp ( ) is Cpmax =0.48 obtained for opt = 8.1 and = 0°.
MPPT CONTROL AND PITCH CONTROL
+
(7)
(8)
= + + (9) As the d and q axis are magnetically decoupled, the ux are given by = . + . (10) = . + . (11) = . + . (12) = . + . (13) Where , and M are the stator ,rotor,and mutual inductances,respectively,with = +M and = + , and are the stator and rotor leakage inductances.
0 0
1
2 3 4 Generator speed (rad/s)
5
6
Fig. 3 Characteristic of the generated power based on the wind speed and generator speed
The Pitch angle control system only starts when the wind speeds is higher than rated wind speed. When the wind speed is in excess of the nominal value, the power extracted from the wind is limited by the pitch control. If the wind speed is less than or equal to nominal value Vr , the switch is in position 1, if not the switch is moved to position 2. The block diagram of pitch angle system is shown in Fig. 4. Where Vw ,Vr ,Prated and Pg are the wind speed, the rated wind speed, the rated power and the generator power respectively.
re
Prated
+
+
PI
-
Tem is controlled by a 3-level hysteresis regulator as shown in Fig. 6, where the states “1” and “-1” (increase/decrease) but ‘0’ to keep Tem.
1 .s
-
Prated 1 Pg 2 Fig4. Block of pitch angle
V.
1 0
CONTROL STRATEGY OF DTC
The proposed control strategy is the Direct Torque Control (DTC) selected for having a simplest structure and the lower parameter dependency compared to the classical solution of the Field Oriented Control method [10]. The principle of DTC is to select proper voltage vectors using a pre-defined switching table. The selection of voltage vectors is based on the hysteresis control of the estimated rotor flux linkage and the estimated torque [11]. Rotor flux linkage estimation
-1
Fig. 6 Three levels hysteresis regulator.
There are eight switching combination six of them are active vectors V1-V6 and two zero vectors V0 and V7.The sector and vector placement is shown in Fig. 7.
( . ) (16) The and estimates components of the r vector obtained by : =
=
=
(
.
.
)
S2
S3 V3(010)
V2(110) r
(17) And
V1(100)
V4(011)
S1
S4
(18)
V0(000) V7(111)
The module and the phase of the rotor flux are given =
=
+
S5
S6
Fig. 7 Control of rotor flux by selection of the voltage vector.
(21)
Select the sector where the rotor flux vector belongs is essential. is controlled by a two-level hysteresis regulator as shown in Fig. 5 ,where the flux amplitude must be increased (K=0) and (K=1) to decrease it [12].
The control table illustrates the set of the switch-state combination according to the state of variable K and KTem and the position sector
TABLE I.
Sector K K =1
K =0
Fig. 5 Two levels hysteresis regulator.
V6(101)
(20)
The torque can be estimated with: =
V5(001)
(19)
KTem KTem=1 KTem=0 KTem=-1 KTem=1 KTem=0 KTem=-1
SWITCHING TABLE
1
2
3
4
5
6
V2 V7 V6 V3 V0 V5
V3 V0 V1 V4 V7 V6
V4 V7 V2 V5 V0 V1
V5 V0 V3 V6 V7 V2
V6 V7 V4 V1 V0 V3
V1 V0 V5 V2 V7 V4
The control scheme of the proposed DTC for a DFIG system is shown in Fig. 8.
Gearbox
Grid DFIG
Vdc Vbc Vab
Ia
Ib
Sa Sb Sc
Switching Table
Transformation : a,b,c ,
m
N
Pitch control
(
=
KTem
K
. )
+-
Prated if vwvr
= .(
|
.
.
|=
+
)
-
+
Tem-ref MPPT
m
Vw Fig.8. Schematic diagram of the control DTC for a DFIG system.
VI. SIMULATION RESULTS 14 13 Wind speed (m/s)
The Simulations of the direct torque control for a large DFIG (1,5 MW) was simulated by using Matlab/Simulink and presented to show the effectiveness of the proposed controls. The parameters of DFIG and the wind turbine used are given in Table (II.III). The figures 9, 10, 11, 12, 13, 14, 15,16 and 17 show results concerning the turbine and DFIG, starting from above: the wind velocity, mechanical power, coefficient power, mechanical speed, tip speed ratio, pitch control, the electromagnetic torque, the rotor flux, the stator and rotor active power, The phase stator voltage and current . The figure 12 shows that the mechanical speed tracks very well the reference. The figures 9 and 10 show that when wind speed is higher than the rated value (12m/s) the mechanical power is limited at its rated value (1,5 MW) by pitch angle system.
Rated wind speed
12 11 10 9 8 0
2
4
6
Time (s) Fig.9. Wind speed and rated wind speed
8
10
6
x 10
0.5
The coefficient power (Cp)
The mechanical power (w)
2
1.5
1
0.5
0 0
2
4
6
8
0.4 0.3 0.2 0.1 0 0
10
Time (s)
Mechanical speed (m/s)
8
10
8
200
Tip speed ratio
6
150
4
100
Pitch angle (degree)
2
50
0
0 -50 0
2
4
6
8
-2 0
10
x 10
2
4
6
8
10
Time (s) Fig.13. Tip speed ratio and the pitch angle.
Time (s) Fig.12. Mechanical speed with its reference. 1.4
4
1.2
0.5
Rotor flux(V.s)
The electromagnetic torque (N.m)
6
10
250
0 -0.5 -1 -1.5 -2 0
4
Time (s) Fig.11. Variation of the coefficient power.
Fig.10. Mechanical power.
1
2
1 0.8 0.6 0.4 0.2
2
4
6
8
Time (s)
Fig.14. electromagnetic torque and its reference
10
0 0
2
4
6
8
Time (s) Fig.15. Rotor flux with its reference
10
6
x 10
Stator voltage (V) Va and current (A) Ia
3
Rotor and Stator power (w)
Active stator power 2
1
0
Active rotor power
-1
-2
-3 0
2
4
6
8
10
Time (s)
Ia 6000 4000 2000 0 -2000 -4000
Va
-6000 -8000 4
4.02
4.04
4.06
4.08
Time (s) Fig.17. First phase current and voltage stator
Fig.16. Active stator and rotor power
VII.
8000
CONCLUSION
A direct torque control strategy for a variable speed wind turbine equipped with DFIG controlled through power converter has been proposed in this paper. This generator side converter is used to capture the maximum wind power with MPPT control strategy. The simulation results are presented for various wind velocities to validate the model and also to show the effectiveness of the proposed control strategy. APPENDIX TABLE II.
PARAMETERS OF TURBINE
Radius
30.66 m
Gear ratio
71.28
Air density
1.22 kg/m3
TABLE III.
DFIG PARAMETERS
Rated power
1.5mw
Stator voltage
690v
Stator resistance
0.0023
Rotor resistance
0.002
Mutual inductance
0.00288 H
Stator inductance
0.00293 H
Rotor inductance
0.00297 H
Number of pole pairs
2
Shaft inertia
18.7 kg.m2
dc-link Voltage
1400 V
REFERENCES
[1]
A.Luna, , F. Kleber, D. Santos,P.Rodríguez, E.H. Watanabe and S. Arnaltes,” Simpli ed Modeling of a DFIG for Transient Studies in Wind Power Applications”, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 1, pp 9-20, 2011. [2] S.Belfedhal, E. Berkouk,” Modeling and Control of Wind Power Conversion System with a Flywheel Energy Storage System”, International Journal Of Renewable Energy Research, IJRER Vol.1, No3, pp.43-52 ,2011 [3] I. Takahashi and T. Noguchi, “A new quick-response and highef ciencycontrol strategy of an induction motor,” IEEE Trans. Ind. Appl., vol. IA-22, no. 5, pp. 820–827, 1986. [4] J. Hu and X. Yuan,” VSC-based direct torque and reactive power control of doubly fed induction generator”, Renewable Energy VOL. 40, pp 1323, 2012 [5] S. Abdeddaim A. Betka,” Optimal tracking and robust power control of the DFIG wind turbine”, I. S. Jacobs and C. P. Bean, “Fine particles, thin films and exchange anisotropy,” in Magnetism, vol. III, G. T. Rado and H. Suhl, Eds. New York: Academic, 1963, pp. 271–350. [6] Endusa Billy Muhando, Tomonobu Senjyu, Aki Uehara, Toshihisa Funabashi, and Chul-Hwan Kim, “LQG Design for Megawatt-Class WECS With DFIG Based on Functional Models' Fidelity Prerequisites,” IEEE Trans. on Energy Conversion, vol. 24, no. 4, pp. 893-904, Dec. 2009. [7] B. Boukhezzar and H. Siguerdidjane,” Nonlinear control with wind estimation of a DFIG variable speed wind turbine for power capture optimization”, Energy Conversion and Management,VOL.50, pp.885892 ,2009. [8] K.Belmokhtar, M.L.Doumbia,and K.Agbossou, “Modélisation et commande d’un système éolien à base de machine asynchrone à double alimentation pour la fourniture de puissances au réseau électrique ‘’, CIGE’10, 03-04 Novembre 2010, Université de Bechar, Algérie [9] K.H.Kim,T.L.Van,D.C.Lee,S.H.Song and E.H.Kim,”Maximum Output power Tracking Control in Variable speed Wind Turbine Systems considering Rotor Inertial Power”,IEEE Transactions On Industrial Electronics,Vol 60,No 8,pp 3207-3217,2013. [10] G. Venu Madhav and Y. P. Obulesu, ’’ Direct Torque Control Strategy for Doubly Fed Induction Machine under Low Voltage Dips’’, IJPEDS, Vol.2, No.4, December 2012, pp. 409-416,2012. [11] A.Essalmi, H Mahmoudi ,“DTC OF PMSM BASED ON ARTIFICIAL NEURAL NETWORKS WITH REGULATION SPEED USING THE FUZZY LOGIC CONTROLLER T,” IC2INT’13,Morocco,FST Settat 2013. [12] Lie Xu, and P Cartwright,” Direct Active and Reactive Power Control of DFIG for Wind Energy Generation”, IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 3, pp.750-758 2006..
